Unraveling the physics of topological phases with random walks of light

I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to emulate intra-atomic interactions and thus analyze many-body effects in topological phases even when using light as the quantum walker. I plan to characterize the intensity probability distribution and the spatial correlations of the output interference pattern for different input states, as well the robustness of localized boundary states characterizing topological insulators to different sources of noise. In particular, I expect to determine whether a non-local order parameter associated with a given topological entanglement measure can be determined in order to characterize topological order, and possible applications in entanglement topological protection. One of the most promising applications of the proposed research includes the study of topological phases in photosynthetic energy transferring processes characterizing biological systems.